Page 18 - Schaum's Outline of Differential Equations

CHAPTER 1

Basic Concepts

DIFFERENTIAL EQUATIONS
A differential equation is an equation involving an nknown function and Ms derivatives.
u
Example 1.1. The follow ins arc differential equations involving the unknown function v,

A differential equation is an ordinary differential equation (ODH) if (he unknown function depends on onl>
one independent \ariahle. If Ihe unknown function depends on two or more independent \ariablcs. the differ-
ential equation is u partial differential t'i/itation (l'l)l-j. With the exceptions of Chapters 31 and 34, the primary
focus of this hook mil he ordinary differential equations.

/
Example 1.2. Hqualions ( ./) through ( / 4) art examples, lil'ordman iliireremial equations, since Ihe unknown funclion v
depends solely on the \ uriubk' .v. hk.|uiui(in (1.5) is LL parti al dillL'renlial equal Kin, si nee v depends on both LliL 1 independent
variables / and T.

The order of a differenlial equation is the order of the highest derivative appearing in the equation.

Example 1.3. Equation l . t ) is a first-order differential equalion- (1.2), (!.4), and (/.5| are second-ordtr differential
(
(
equations. [Note in (1.4) that the order of the highest derivative appearing in Ihe equation is t\vo.| Equation l.j) is a third-
order differential equation.
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